Stochastic Volatility Modeling
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Stochastic Volatility Modeling
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Author : Lorenzo Bergomi
language : en
Publisher: CRC Press
Release Date : 2015-12-16
Stochastic Volatility Modeling written by Lorenzo Bergomi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-16 with Business & Economics categories.
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Modelling And Simulation Of Stochastic Volatility In Finance
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Author : Christian Kahl
language : en
Publisher: Universal-Publishers
Release Date : 2008
Modelling And Simulation Of Stochastic Volatility In Finance written by Christian Kahl and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Business & Economics categories.
The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
Handbook Of Volatility Models And Their Applications
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Author : Luc Bauwens
language : en
Publisher: John Wiley & Sons
Release Date : 2012-03-22
Handbook Of Volatility Models And Their Applications written by Luc Bauwens and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-22 with Business & Economics categories.
A complete guide to the theory and practice of volatility models in financial engineering Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency. Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility: Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.
Statistical Analysis Of Stochastic Processes In Time
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Author : J. K. Lindsey
language : en
Publisher: Cambridge University Press
Release Date : 2004-08-02
Statistical Analysis Of Stochastic Processes In Time written by J. K. Lindsey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-02 with Mathematics categories.
This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
The Volatility Smile
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Author : Emanuel Derman
language : en
Publisher: John Wiley & Sons
Release Date : 2016-09-06
The Volatility Smile written by Emanuel Derman and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-06 with Business & Economics categories.
The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.
Uncertain Volatility Models
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Author : Robert Buff
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-10
Uncertain Volatility Models written by Robert Buff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-10 with Mathematics categories.
This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
The Volatility Surface
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Author : Jim Gatheral
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-10
The Volatility Surface written by Jim Gatheral and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-10 with Business & Economics categories.
Praise for The Volatility Surface "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP
Option Valuation Under Stochastic Volatility
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Author : Alan L. Lewis
language : en
Publisher:
Release Date : 2000
Option Valuation Under Stochastic Volatility written by Alan L. Lewis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Business & Economics categories.
Stochastic Volatility
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Author : Neil Shephard
language : en
Publisher: Oxford University Press, USA
Release Date : 2005
Stochastic Volatility written by Neil Shephard and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Business & Economics categories.
Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This work brings together some of the main papers that have influenced this field, andshows that the development of this subject has been highly multidisciplinary.
Applied Quantitative Finance For Equity Derivatives
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Author : Jherek Healy
language : en
Publisher:
Release Date : 2017-09-21
Applied Quantitative Finance For Equity Derivatives written by Jherek Healy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-21 with categories.
This book presents the most significant equity derivatives models used these days. It is not a book around esoteric or cutting-edge models, but rather a book on relatively simple and standard models, viewed from the angle of a practitioner. Most books present models in an abstract manner, often disconnected from how to apply them in the real world. This book intends to fill that gap, with the ambitious goal of transforming a reader unfamiliar with equity derivatives models into a specialist of such models. What's special about it? The subject of cash dividends is absent of most books, and yet a real practical problem that every equity derivatives desk faces. This books gives a thorough treatment of the subject, be it for European, American, or more exotic options under the local volatility model. Similarly, Dupire local volatility issues are usually ignored while everybody face them. It presents various refinement for numerical techniques, for example, how to properly handle barriers in the TR-BDF2 finite difference method (and others) for a maximum accuracy, how to actually perform the parametric or non-parametric regression for American options in Monte-Carlo, how to do randomized Monte-Carlo simulations, which random number generators are pertinent these days, how to apply quasi Monte-Carlo to the particle stochastic-local-volatility calibration method,which quadrature should use consider for variance swap, volatility swap or vanilla options under stochastic volatility models with known characteristic function... It covers VIX options and dividend derivatives. The backward/forward representation of exotics is well known in the industry and yet rarely presented. It does not cover esoteric payoffs that might have a nice analytical formula but are never traded in practice, or models too complex to be practical.